Localizing prime idempotent kernel functors
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- by S. K. Sim PDF
- Proc. Amer. Math. Soc. 47 (1975), 335-337 Request permission
Abstract:
In this note, we call a prime idempotent kernel functor a localizing prime if it has the so-called property (T) of Goldman. We generalize a theorem of Heinicke to characterize localizing prime idempotent kernel functors and present an example of a prime idempotent kernel functor on $\operatorname {Mod-}R$, the category of unitary right $R$-modules, which is not a localizing prime, even though $R$ is a right artinian ring.References
- Oscar Goldman, Rings and modules of quotients, J. Algebra 13 (1969), 10–47. MR 245608, DOI 10.1016/0021-8693(69)90004-0
- A. G. Heinicke, On the ring of quotients at a prime ideal of a right noetherian ring, Canadian J. Math. 24 (1972), 703–712. MR 299633, DOI 10.4153/CJM-1972-066-2
- Joachim Lambek and Gerhard Michler, The torsion theory at a prime ideal of a right Noetherian ring, J. Algebra 25 (1973), 364–389. MR 316487, DOI 10.1016/0021-8693(73)90051-3
- B. L. Osofsky, A generalization of quasi-Frobenius rings, J. Algebra 4 (1966), 373–387. MR 204463, DOI 10.1016/0021-8693(66)90028-7
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 335-337
- MSC: Primary 16A62
- DOI: https://doi.org/10.1090/S0002-9939-1975-0369436-7
- MathSciNet review: 0369436